Having been fortunate to observe a variety of math classrooms, especially within the independent school sector, we’ve come to learn a number of things, which we will write about across several blog posts. This blog post is about the need to focus on metacognitive instruction and skill-building in K-8 mathematics classes.
Metacognition research has assisted educators in changing the way we view learning. We know high achieving students usually apply metacognitive processes in their learning and problem solving. And students who apply metacognitive processes tend to be higher achievers. Recent studies have shown that even young children can apply metacognitive processes when the tasks fit their interests and capabilities. And rather than seeing development of these skills as purely age-related, instead we know that it may likely be due to lack of appropriate exposure in school.
Also key is the finding that metacognition is domain-specific, and thus learning environments must cultivate the domain-specific metacognitive tools kids need in order to achieve at high levels within the domain.
Looking specifically at mathematics, kids need classrooms in which high level cognitive processes are expected of them and work with CUN problems (complex, unfamiliar, and non-routine) is the core practice. They need classrooms in which mathematics is presented as a coherent set of ideas, not disparate “units” or skills that present a fragmented discipline. Kids need teachers who will coach, model, and name strategies that will assist students with their metacognitive development. And they need daily opportunities to attempt to do this difficult work of metacognition within the domain of mathematics.
Based on our experience, this rarely happens, even in the many expensive and well-resourced independent school classrooms.
The only way to teach the type of mathematics problem-solving appropriate for innovation-driven societies is by giving kids the opportunity to learn complex mathematics daily, starting at the beginning of their mathematics career. In many, many classrooms our kids are spending most of their precious academic minutes on low-level tasks such as repeatedly applying a procedure, memorizing a rule, or trying to mimic the teacher’s method of solving a problem. Any metacognitive coaching is reduced to acronyms the child can use to memorize a rule (ex. FOIL), or choral recitation, or very brief bouts of metacognitive coaching within assigned tasks that actually only require low cognitive demand. Rarely are classrooms providing the rich mathematics instruction that is the territory for practicing metacognitive skills, and rarely are teachers providing children with the support they need to struggle to understand the metacognitive skills and processes suitable for comprehending, applying, and creating with the math expected in innovation-driven societies.
Focused effort on the part of schools can ensure that mathematics instruction reaches a higher level and includes domain specific metacognitive instruction and skill-building.